Linear Versus Exponential Change

Learn and apply linear versus exponential change using equations, examples, and interpretation.

Lesson 5 of 53 parts Practice Flashcards

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Constant Difference

Objective: Explain and use constant difference in an Algebra 1 problem.

A linear pattern has equal output differences for equal input steps. Generally no.

Worked examples

Try itExample 1.1: A linear pattern starts at 13 and gains 2 each step. What is its value after 5 steps?Show answer

23. Add the fixed step once per period. The answer is 23.

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Constant Difference

Objective: Explain and use constant difference in an Algebra 1 problem.

A linear pattern has equal output differences for equal input steps. Generally no.

Worked examples

Try itExample 1.1: A linear pattern starts at 13 and gains 2 each step. What is its value after 5 steps?Show answer

23. Add the fixed step once per period. The answer is 23.

Constant Ratio

Objective: Explain and use constant ratio in an Algebra 1 problem.

An exponential pattern has equal output ratios for equal input steps, provided values and ratios are defined. Generally no.

Worked examples

Try itExample 2.1: A quantity starts at 23 and increases by factor 3 per period. What is its value after 8 periods?Show answer

150903. Multiply the initial amount by the factor once per period. The answer is 150903.

Model Selection

Objective: Explain and use model selection in an Algebra 1 problem.

A short table can support several models, so check differences, ratios, units, and context before extending a rule. The original pattern may not continue.

Worked examples

Try itExample 3.1: A linear pattern starts at 33 and gains 4 each step. What is its value after 11 steps?Show answer

77. Add the fixed step once per period. The answer is 77.

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